Reception of a signal modulated according to a multilevel coding technique

ABSTRACT

A method for receiving a signal modulated according to a multilevel coding technique, comprising at least two coding levels each having different noise robustness, said signal including a plurality of symbols each comprising at least one bit, assigned to one of said coding levels, said method comprising at least one decoding iteration including successive steps of decoding each of said received bits, at least one of said decoding steps integrated the result of at least one possible previous decoding step. The invention is characterized in that it consists in decoding said bits according to a predetermined sequence taking into account the robustness of said levels, the bit(s) assigned to the decoding level having the higher noise robustness, called most robust level, being decoded first.

CROSS-REFERENCE TO RELATED APPLICATION

This Application is a Section 371 National Stage Application ofInternational Application No. PCT/FR2003/002878, filed Oct. 1, 2003 andpublished as WO 2004/032397 A1 on Apr. 15, 2004, not in English, whichis based on French Application No. 02/12158, filed on Oct. 1, 2002, thecontents of which is hereby incorporated by reference in its entirety.

FIELD OF INVENTION

The field of the invention is that of signal processing and digitalcommunications.

BACKGROUND OF THE INVENTION

More specifically, the invention relates to a technique to optimize thedecoding of a signal modulated according to a multi-level coding or MLCtechnique.

To date, there are several known coded-modulation channel-codingtechniques. Indeed, following Ungerboeck's discovery of lattice-codedmodulation also known as MCT (“Channel Coding with Multilevel/PhaseSignals”), described in IEEE Trans. IT, January 1982, 28, No. 1, pp.55-67), block-coded modulation or BCM and trellis-coded multidimensionalmodulation have been proposed.

BCM type modulation has been described especially by Cusack in “Errorcontrol codes for QAM signaling>>, Electronics Letter, January 1984, 20,pp. 62-63 and Sayegh in “A class of optimum block codes in signalspace”, IEEE Trans. COM, October 1986, 34, No. 10, pp. 1043-1045.

Trellis-coded multidimensional modulation has been described especiallyby Wei in “Trellis-coded Modulation with MultidimensionalConstellations”, IEEE Trans. IT, July 1987, 33, n°4, pp. 483-501 and byCalderbank and Sloane in “New trellis codes based on lattices andcosets”, IEEE Trans. IT, March 1987, 33, No. 2, pp. 177-195.

Moderately complex trellis-coded modulation (typically with 4 or 8states) may give a coding gain of 3 to 4 dB. However, in applications ofhigh-capacity RF beams, the implementation of the Viterbi decoder, whichis necessary to decode the modulation, is still very costly.

A new family of BCM codes is therefore being proposed for theseparticular applications. Such codes are simpler to implement, but theircoding gain is generally limited to 2 dB.

An attractive coding technique for high-capacity RF beam applicationshas been proposed by Imai and Hirakawa in “A new multilevel codingmethod using error-correction codes” IEEE Trans. IT, May 1977, 23, No.3, pp. 371-377. This is a technique of multi-level coding whose valuelies in the existence of a simple step-by-step coding method, entailingan efficient compromise between performance and complexity ofimplementation.

Here below, a brief description is given of the principle of multi-levelcoding as well as the associated method of step-by-step decoding.

We consider a 2^(m)-point constellation A₀ capable, therefore, oftransmitting m bits per symbol.

If m designates the number of bits to be coded, the constellation A₀ ispartitioned into m levels, thus giving 2^(m) subsets. The principle ofthis partition is identical to the one defined by Ungerboeck, and servesto maximize the minimum Euclidean distance in the subsets of thepartition. If d_(i) designates the minimum Euclidean distance in thesubsets obtained at the i^(th) partition level, the following inequalitymust be verified:d₀<d₁<d₂< . . . <d_(m)  (1)where d₀ is the minimum distance in the constellation A₀.

Thus, the m bits b₁, b₂, . . . , b_(m), where b_(i) is the bit assignedto the i^(th) level of the partition, select a subset among the 2^(m)subsets. FIG. 1 gives a diagram of this partition where m=2. A₀ ispartitioned first of all into two subsets B_(i), i∈·{0, 1} and wherei=b₁, with a minimum distance d₁, then into four subsets C_(i), i∈{0, 1,2, 3} and where i=b₁+2b₂, with a minimum distance d₂. If A₀ is a squareconstellation with a Euclidean distance d₀, then d₁=√{square root over(2)}d₀ and d₂=√{square root over (2)}d₁=2d₀.

This process of assigning points of the constellation A₀ is aimed atclassifying the m bits that represent the symbol sent as a function oftheir vulnerability to noise. Indeed, it can be seen that the bit b₂ isless vulnerable than the bit b₁, since there is a minimum Euclideandistance of d₂>d₁ corresponding to it. According to the relationship(1), it can be shown that, if the bits b_(k), k=i−1 are sufficientlyprotected so that they are accurately received, the bit b_(i),i=m isbetter protected from noise than the other bits b_(j), j<i. It wastherefore envisaged to code these bits separately with different codes.

This is the principle of multi-level coding which, after partitioningthe constellation A₀ into m levels, consists in using m coders E_(i),i=1, . . . , m, to protect these m bits with several levels ofprotection.

In other words, the principle of multi-level coding relies on the jointoptimization of the coding and of the modulation, enabling improvedtransmission performance to be achieved. Thus, in the context of a QAM(“Quadrature Amplitude Modulation”), greater protection is given to thebits which, owing to their position in the QAM mapping, are more likelyto be affected by error. The protection given to the different bitsdepends on the coding used.

The pattern of this coding concept is illustrated in FIG. 2. The datastream to be transmitted, at a bit rate D, is divided by theseries-parallel conversion block 21 into m streams with a bit rateD_(i), i=1, . . . , m. The m first strings are coded by m binary codesE_(i)(n_(i), k_(i), d_(i)), i=1, . . . , m, referenced 22, with a codingrate R_(i)=k_(i)/n_(i) and a minimum Hamming distance d_(i). At theinput to the modulator 23, the m binary strings must be synchronous,with a bit rate D′/m. It is therefore possible to define an equivalentcoding rate R given byR=D/D′  (2)

If it is assumed that all the n_(i) values are equal, giving n_(i)=n,i=1, . . . , m, and that the m codes E_(i) are block codes, this codingcan be described by a matrix structure identical to the one used for theBMCs described especially by Sayegh in the article mentioned here above.A code word contains n symbols and may be represented by a matrix of mrows and n columns where the j^(th) column represents the binaryassignment of the j^(th) symbol of the block, and the i^(th) rowrepresents the i^(th) partition level. The row i, i=1, . . . , m is acode word E_(i) (n_(i), k_(i), d_(i)). The minimum Euclidean distance dobtained with this coding is given byd ²=min_(i=1 . . . , M+1)(d _(i) d _(i−1) ²), with d _(m+1)=1.  (3)

Knowing that the d_(i) values verify the above relationship (1), themulti-level coding is optimized if:d₁>d₂> . . . >d_(m).  (4))It has therefore been determined that the bit b₁ had to be the mostprotected bit, then b₂ etc. This matrix description can be generalizedto the case where the codes would be any codes whatsoever. If the n_(i)values are not identical, it is enough to consider a matrix with m rowsand l columns where l is the least common multiple of the n_(i) values,i=l, . . . , m. In the particular case where one of the codes is theconvolutive code, the matrix to be considered is semi-infinite.

The decoding method classically used in association with a multi-levelcoding of this kind is a sub-optimal step-by-step decoding, which hasthe advantage of being very simple to implement.

According to this technique, the decoding method is done step-by-stepwhere each bit is decoded independently by a simple decoder working onhard decisions but where the output of the decoder (i) may make acorrection on the bits at the input of the decoder (i+1). FIG. 3 gives ablock diagram of this type of decoder, where m=2. Given (r₁, r₂, . . . ,r_(n)) the block 31 of n symbols received at the input of the decoder,the decoding operation is performed in the following successive steps:

-   -   first of all the n bits b^(i) ₁, i=1, . . . , n assigned to the        first partitioning level (A₀) are decoded: a hard decision 32 in        A₀ is effected every r_(i), i=1, . . . , n. Thus a first        estimation of b^(i) ₁, i=1, . . . , n, is obtained written        {tilde over (b)}₁ ^(i), i=1, . . . , n. A hard-decision decoding        33 working on {tilde over (b)}₁ ^(i), i=1, . . . , n gives a        final estimation written {tilde over (b)}₁ ^(i), i=1, . . . , n.    -   then the n bits b^(i) ₂, i=1, . . . , n. assigned to the second        partition level (B₀ or B₁) are decoded: as a function of the        bits {tilde over (b)}₁ ^(i), i=1, . . . , n which are encoded by        the same encoder used at transmission, a second decision        operation 34 is effected on the symbols r_(i), i=1, . . . , n in        the subsets B_(pi) with p_(i)={tilde over (b)}₁ ^(i) for i=1, .        . . , n. The bits {tilde over (b)}₂ ^(i), i=1, . . . , n        obtained are decoded by the decoder “2” referenced 35 to give a        final decision {tilde over (b)}₂ ^(i), i=1, . . . , n.    -   finally, the remaining non-coded bits are decoded: from the bits        {circumflex over (b)}₁ ^(i), {circumflex over (b)}₂ ^(i), i=1, .        . . , n, recoded by their associated coder, a third detection 36        is made of r_(i), i=1, . . . , n, in the subsets of the second        partition level C_(i), i=1, . . . , n. Thus, an estimation of        the m−2 remaining non-coded bits is obtained for each of the        symbols r_(i), i=1, . . . , n.

According to the decoding technique associated with multi-level codingor MLC, the first decoding is therefore done systematically in thesubset A₀ of the constellation. The result of this decoding is thenexploited for the decoding of the next subset B₀. A decoding techniqueof this kind is described especially in the article by L. Papke and K.Fazel, “Different Iterative Decoding Algorithms for CombinedConcatenated Coding and Multiresolution Modulation” on the terrestrialbroadcasting of television signals, coded according to a multi-levelcoding technique. More specifically, this document by Papke describes asolution based on multi-level coding and decoding to obtain threestreams related to three different services, the SDTV stream being morerobust than the EDTV stream, which is itself more robust than the HDTVstream. This Papke technique is aimed at protecting the most importantstreams, in accentuating the robustness of the level with which they areassociated. In practice, according to the Papke decoding technique, anestimation is made first of all of the u_(i) ¹ bits assigned to the2^(m)-point constellation, then the u_(i) ² bits assigned to the subsetsof the constellation corresponding to u_(i) ¹, etc.

Now, for an MLC to be optimal, the decoding gain that must be obtainedbetween the different coding levels is 6 dB, which is very difficult toobtain.

One drawback of this prior art technique therefore is that the decodingmethod conventionally implemented in the context of MLC coding showsmediocre performance.

In particular, such a technique of sub-optimal step-by-step decoding ispoorly adapted to channels presenting additive Gaussian noise andDoppler-affected multiple-path channels.

It is a goal of the invention especially to overcome these drawbacks ofthe prior art.

SUMMARY OF THE INVENTION

More specifically, it is a goal of the invention to provide a techniquefor the decoding of a signal modulated according to an MLC codingtechnique, having improved performance compared with the prior arttechniques.

It is another goal of the invention to implement such a technique, thatenables a reduction in the binary error rate (or BER) as compared withthe sub-optimal decoding technique of the prior art.

It is also a goal of the invention to provide a technique of this kindthat is simple and costs little to implement, and is suited todisturbance-prone channels, and especially to channels showing Gaussianadditive noise and Doppler-affected multiple-path channels.

These goals, as well as others that shall appear here below, areachieved by means of a method for the reception of a signal modulatedaccording to a multi-level coding technique, comprising at least twocoding levels each having a distinct noise robustness. Such a signal hasa plurality of symbols each comprising at least one bit, assigned to oneof said coding levels, and such a reception method comprises at leastone iteration of decoding comprising successive steps for the decodingof each of the bits received, at least one of said decoding steps takingaccount of the result of said at least one possible preceding step ofdecoding.

According to the invention, said bits are decoded in a predeterminedorder taking account of the robustness of said levels, the bit or thebits assigned to the coding level that have the greatest noiserobustness, called the most robust level, being decoded first.

Thus, the invention is based on a wholly novel and inventive approach tothe decoding of a signal modulated according to a technique ofmulti-level coding. Indeed, unlike in the sub-optimal decoding methodused in the prior art, the invention proposes to perform a decoding ofthe different partition levels that takes account of the vulnerabilityof these levels to noise. Thus, the most robust level is decoded first,in order to be able to then propagate the result of the decoding fromthis level to the less robust levels. Thus, the decoding performanceobtained is highly improved as compared with the sub-optimal decodingtechniques of the prior art.

Advantageously, said predetermined order corresponds to the decreasingorder of the robustness of the coding levels to which said received bitsare assigned.

Preferably, each of said successive decoding steps takes account of theresult of said preceding decoding step or steps so as to improve theresult of said steps for the decoding of said bits assigned to the lessrobust levels.

Thus, the result of the decoding of the bits of a given level ofrobustness is systematically exploited during the decoding of the bitsof the directly lower robustness level, thus greatly improving theconfidence that may be given placed to this second decoding.

According to one advantageous embodiment of the invention, said bitsassigned to said most robust level are the most significant bits of saidcorresponding symbol.

This alternative embodiment corresponds especially to the particularmode of implementation chosen by the standardization consortium DRM(Digital Radio Mondiale as presented in the document ETSI ES 201 980V1.2.1 (2002-07)).

Preferably, within one of said decoding iterations, each of saidsuccessive steps for the decoding of said received bits is preceded by acorresponding demodulation step.

The received bits are therefore first demodulated and then decoded.

Advantageously, a reception method of this kind comprises at least twosuccessive decoding iterations, one step for decoding the bits of agiven level taking account, during the n^(th) iteration where n≧2, ofthe result of at least certain of said steps of decoding of saidreceived bits assigned to the coding levels less robust than said givenlevel, and implemented during at least one of said preceding iterations.

Thus, in a particular case comprising three coding levels, the decodingof the bits of the most robust level takes account especially, duringthe second iteration, of the result of the decoding of the bits of thetwo least robust levels obtained during the first iteration.

Preferably, a reception method of this kind has two successive decodingiterations.

Indeed, the inventors have noted that the increase in performanceresulting from the implementation of a third iteration was low or, atthe very least, negligible in relation to the corresponding increase incomplexity.

Advantageously, at the end of at least certain of said iterations, areception method of this kind implements a step for the estimation of asent symbol, and a step for the computation of an extrinsic piece ofinformation taking account of said estimated sent symbol, said extrinsicpiece of information enabling an improvement in the result of said stepsfor the decoding of said following iteration or iterations.

Thus, after the first decoding iteration, a piece of extrinsicinformation will be computed and will be used during the second decodingiteration, in order to heighten its performance.

Advantageously, said piece of extrinsic information has the form: α(S_(r)-S_(e)), where α∈[0, 1], S_(r) is said received symbol and S_(e) issaid estimated sent symbol.

In the particular case where two successive iterations are implemented,the extrinsic information is therefore proportional to the differencebetween the received symbol and the symbol estimated from the decodedbits of the different levels during the first iteration. This differenceis weighted by a characteristic coefficient of the confidence given tothe decoding.

In a first advantageous embodiment of the invention, α is substantiallyequal to 0.25.

Such a value of a makes it possible to obtain satisfactory performanceduring the second decoding iteration for most of the transmissionchannels considered.

In a second advantageous embodiment, a reception method of this kindcomprises a step to optimize the value of α as a function of thesignal-to-noise ratio.

By means of the coefficient α, it is indeed possible to choose to placea higher or lower degree of confidence, in the extrinsic piece ofinformation, in the estimated sent symbol, in order to take account ofit to a greater or lesser degree during the following coding iterations.The optimization of the value of a as a function of the signal-to-noiseratio leads to values of α close to 1 when the signal-to-noise ratio isvery high, and to values close to 0 when the contrary is the case.

According to an advantageous characteristic of the invention, such areception method furthermore comprises a step for determining asignal-to-noise ratio from at least one piece of reference informationsent, called pilot information, the value of which is known a priori inreception.

It may be recalled, indeed, that a classic technique to estimate thetransmission channel in OFDM, for example, consists of the insertion ofreference carriers, at positions known to the receiver, into the streamof payload carriers. At reception, the values taken by these referencecarriers, called pilot carriers, are read and the complex gain of thechannel at these reference positions is easily deduced therefrom. Thecomplex gain of the channel is then derived on all the points of thetime-frequency network transmitted, from the computed value of thecomplex gain at the reference positions.

A pilot-based mechanism of this kind can therefore be used, in theframework of the invention, to determine the signal-to-noise ratio andtherefore optimize α. It is used especially in the DVB-T standard(“Digital Video Broadcasting (DVB); Framing Structure, Channel Codingand Modulation for Terrestrial Television (DVB-T) standard, ETS 300 744,March 1997).

According to an advantageous embodiment of the invention, such areception method furthermore comprises, for at least certain of saidcoding levels, an additional de-interleaving step implemented betweenthe said steps for the modulation and decoding of said received bits.

An embodiment of this kind can be used especially to improve theperformance of the reception method relative to the Doppler-affectedtransmission channels.

The invention also relates to a method for the decoding of a signalmodulated according to a multi-level coding technique, comprising atleast two coding levels each having a distinct noise robustness, saidsignal comprising a plurality of symbols each comprising at least onebit, assigned to one of said coding levels, said method comprising atleast one iteration of decoding comprising successive steps of decodingof each of said bits received, at least one of said decoding stepstaking account of the result of said at least one preceding step ofdecoding if any.

According to the invention, said bits are decoded in a predeterminedorder taking account of the robustness of said levels, the bit or thebits assigned to the coding level that have the greatest noiserobustness, called the most robust level, being decoded first.

The invention also relates to a device for the reception of a signalmodulated according to a multi-level coding technique, comprising atleast two coding levels each having a distinct noise robustness, saidsignal comprising a plurality of symbols each comprising at least onebit, assigned to one of said coding levels, said device comprisingdecoding means implementing a successive decoding of each of said bitsreceived, the decoding of at least one of said bits received takingaccount of the result of said at least one preceding decoding operationif any.

According to the invention, said decoding means decode said bits in apredetermined order taking account of the robustness of said levels, thebit or the bits assigned to the coding level that have the greatestnoise robustness, called the most robust level, being decoded first.

The invention also relates to a system for the coding/decoding of asignal comprising a plurality of symbols each comprising at least onebit, assigned to one of said coding levels.

Such a system comprises at least one coding device enabling themodulation of said signal according to a multi-level coding technique,comprising at least two coding levels each having a distinct noiserobustness, and at least one decoding device comprising decoding meansimplementing a successive decoding of each of said received bits, thedecoding of at least one of said received bits taking account of theresult of at least one previous decoding if any, said decoding meansdecoding said bits in a predetermined order taking account of therobustness of said levels, the bit or bits assigned to the coding levelthat show the greatest noise robustness, called the most robust level,being decoded first.

The invention finally relates to the applications of the receptionmethod described here above to at least one of the following fields:

-   -   digital radio transmission, especially of the DRM (“Digital        Radio Mondiale”) type;    -   error corrector codes;    -   digital signal processing;    -   digital communications;    -   the recording/playback of a digital signal.

Other features and advantages of the invention shall appear more clearlyfrom the following description of a preferred embodiment, given by wayof a simple, non-exhaustive illustrative example and from the appendeddrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1, already described with reference to the prior art, shows anexample of a partition of a constellation A₀ into m levels, giving 2^(m)subsets when m=2;

FIG. 2, already described with reference to the prior art, is a blockdiagram of a multi-level coder;

FIG. 3 already described with reference to the prior art, is a blockdiagram of the step-by-step decoder implemented in the prior art, inassociation with the multi-level coder of FIG. 2, in the case of athree-level coding;

FIG. 4 presents a comparison of the robustness of different levels ofMLC coding as a function of a Gaussian additive white noise;

FIG. 5 is an example of a receiver according to the invention, carryingout the optimized decoding of a QAM64 symbol with two iterations and theuse of the extrinsic information;

FIG. 6 illustrates the comparative decoding performance of the MLCtechniques according to the sub-optimal decoding method of the prior artand the decoding method of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The general principle of the invention relies on taking account of thenoise robustness of the different coding levels of a signal modulatedaccording to a multi-level coding MLC technique, to determine the orderof decoding of the received bits.

Referring to FIG. 4, we present the concept of robustness of an encodinglevel, in the context of a multi-level coding or MLC technique.

The robustness of a coding level may be illustrated by the curve of thebinary error rate of this level, and the function of the signal-to-noise(S/N) ratio: throughout the document, a coding level shall be consideredto be all the more robust as the binary error rate associated with it islow.

By decoding each coding level independently, i.e. without making anyreturn loop from one level to another (in other words, the result of thedecoding of one level is not used in the decoding of the next level)),it is possible to determine the level of noise robustness of each level.More particularly, FIG. 4 illustrates the robustness of each MLC codinglevel relative to a Gaussian additive white noise.

Thus, the DRM (Digital Radio Mondiale) standardization as presented inthe document ETSI ES 201 980 V 1.2.1 (2002-07) has chosen multi-levelcoding MLC for the broadcasting of a digital signal in the AM (AmplitudeModulated) bands whose frequencies are below 30 MHz. One of the modeschosen by DRM comprises a 64QAM (Quadrature Amplitude Modulation) withan overall coding efficiency of R=0.6 with R_(MSB)=0.8 R_(ISB)=0.67 andR_(LSB)=0.33, where MSB represents the set of the most significant bits,LSB represents the set of the least significant bits and ISB representsthe set of the intermediate significant bits.

Thus, a point of the 64QAM corresponds to a set of bits, namely one bitassigned to the MSB level, one bit to the ISB level, and one bit to theLSB level.

In decoding the three QAM modulation levels, namely MSB, ISB and LSB, itis observed that the most robust level is the one corresponding to theMSBs (curve referenced 41), then to the LSBs (curve referenced 42) andfinally to the intermediate level bits or ISBs (curve referenced 43), asillustrated in FIG. 4. Indeed, the BER curve 41 associated with the MSBlevel is the one that falls most rapidly as a function of thesignal-to-noise (S/N) ratio, and the BER curve 43 associated with theISB level is the one that decreases most slowly as a function of thesignal-to-noise (S/N) ratio.

However, it is possible to again analyze the performance of the ISB andLSB levels by looping back from the most robust level (MSB), i.e. intaking the result of the decoding of the MSB level into account in thedecoding of the ISB and LSB levels.

It can be seen then that the ISB level becomes the second most robustlevel, before the LSB level: thus, the decreasing order of robustness ofthe coding levels is MSB-ISB-LSB.

According to the technique proposed by the invention, the optimum orderof the decoding of the MLCs is therefore the decreasing orderMSB-ISB-LSB.

Referring now to FIG. 5, we present an exemplary embodiment of areceiver according to the invention.

The working of such a receiver is based on four main principles:

-   -   the first principle is based on the modulation, and then the        decoding, first of all of the most robust level, the result of        such a decoding enabling an improvement in the demodulation, and        hence the decoding, of the less robust levels. This operation is        repeated until the least robust encoding level;    -   the second principle implemented by a receiver according to the        invention is that of an iterative process. Indeed, after        demodulation and decoding of all the levels, the operation may        be repeated so as to improve the demodulation of the most robust        level by means of the result of the decoding of the lower        levels;    -   the third principle of operation relies on the implementation of        a test of the relevance of the correction of the modulated        signal as a function of the amplitude of the corrective signal        relative to the signal to be demodulated;    -   finally, such a receiver uses a piece of extrinsic information,        between each iteration, in order to improve the demodulation and        hence the decoding of the received signal.

These four principles are presented in greater detail with reference toFIG. 5, which presents a particular embodiment, in the context of aQAM64 (Quadrature Amplitude Modulation) modulation. It will of course beeasy for those skilled in the art to extend this description to any typeof multi-level modulation.

In the particular embodiment of FIG. 5, the most robust levelcorresponds to the level of coding of the most significant bits (MSB)and the least robust level corresponds to the least significant bits(LSB). As explained here above with reference to FIG. 4, the noiserobustness of a coding level is inversely proportional to the error rateof this level. Furthermore, the error rate is a function of theefficiency of the coding, the power associated with each bit (alsocalled the level of the bit) and the signal-to-noise ratio (indeed, theerrors observed in the signal depend of course on the noise that affectsit).

It will therefore easily be understood that the most robust level is notnecessarily the level of the most significant bits. By way of anillustration, however, the following description shall focus especiallyon the presentation of an embodiment of the invention in this particularcase.

The receiver of FIG. 5 has two stages referenced 51 and 52,corresponding to two successive decoding iterations. Indeed, theinventors have observed that the improvement in decoding performanceresulting from the implementation of the third decoding iteration is lowand thus, in the preferred embodiment of the invention, only twoiterations of the decoding process are implemented. Thus an efficientcompromise is obtained between performance and complexity.

We describe first of all the first decoding stage referenced 51. Thisstage is supplied with the received QAM64 symbol, also called S_(r),which is distributed to the three demodulators referenced 511 to 513,respectively providing for the MSB, ISB and LSB demodulations. Thereceived symbol S_(r) is formed by three bits X_(RMSB), X_(RISB),X_(RLSB) respectively assigned to the MSB, ISB and LSB levels, which maybe expressed in the form: S_(r)=X_(RMSB)+X_(RISB)+X_(RLSB).

The first step implemented at the reception of the symbol S_(r) consistsin demodulating the bits assigned to the most noise-robust level, i.e.in this case the most significant bits (MSB). Thus, at output of thedemodulator 511, the demodulated bits {tilde over (b)}₃ ^(i), i=1, . . ., n, which supply the decoder referenced 514 are obtained. Afterdecoding by the decoder 514, the decoded bits {tilde over (b)}₃ ^(i),i=1, . . . , n are obtained.

The second step consists in coding the decoded bits {circumflex over(b)}₃ ^(i), i=1, . . . , n with the coder used at transmission, calledthe “coder 3”, referenced 517. The bits thus coded are fed to the ISBdemodulator referenced 512, which takes account of them to demodulatethe intermediate significant bits (ISB) {tilde over (b)}₂ ^(i), i=1, . .. , n. The demodulated intermediate significant bits are given at inputof the decoder referenced 515 which, after decoding, delivers thedecoded intermediate significant bits {circumflex over (b)}₂ ^(i), i=1,. . . , n. It will be noted that the ISB coding level here is theintermediate noise robustness level and that it is therefore demodulatedand decoded directly after the MSB level.

The decoded intermediate significant bits {circumflex over (b)}₂ ^(i),i=1, . . . , n, are furthermore given at input of the coder referenced518, which is identical to the coder used at transmission for the ISBlevel.

By using the recorded bits of the upper levels of robustness (MSB andISB), it is then possible to demodulate the bits of the less robustlevel which, in the preferred embodiment described with reference toFIG. 5, corresponds to the level of the least significant bits (LSB).

To do this, the LSB demodulation device referenced 513 is supplied withthe re-coded bits coming from the coders referenced 517 and 518 of themore robust MSB and ISB levels, and delivers the demodulated leastsignificant bits, {tilde over (b)}₁ ^(i), i=1, . . . , n. After decodingby the decoder referenced 516, the decoded least significant bits{circumflex over (b)}₁ ^(i), i=1, . . . , n, are obtained.

The decoded least significant bits {circumflex over (b)}₁ ^(i) mayfurthermore feed the coder referenced 519, which is identical to thecoder used at transmission for the LSB level.

After decoding of the three levels of the QAM level, it is possible todetermine (520) an estimation of the symbol sent, from the recoded bitsdelivered by the three coders referenced 517 to 519.

Thus, in the particular embodiment described in relation to FIG. 5, thesymbol S_(e) sent has the form S_(e)=4b_(MSB)+2b_(ISB)+b_(LSB), whereb_(MSB), b_(ISB) and b_(LSB) respectively correspond to the bits of theMSB, ISB and LSB levels.

From the estimated symbol sent, the Euclidean distance between the sentsymbol S_(e) and the received symbol S_(r), is computed in weightingthis distance by a coefficient α (0<α<1). Thus an extrinsic piece ofinformation a(S_(r)-S_(e)) 521 is determined. This extrinsic piece ofinformation can be used in the second state 52 of the receiver toimprove the decoding of the following iterations.

The second decoding stage 52 works similarly to the first stagereferenced 51. It has especially three demodulation devices referenced521 to 523, and three decoders referenced 524 to 526 respectivelyassociated with the three coding levels MSB, ISB and LSB.

The first step implemented within this stage 52 is the demodulation ofthe most robust MSB level by the block referenced 521. Such a block 521is supplied, firstly, by the recorded bits of the less robust levels,ISB and LSB, coming from the coders referenced 518 and 519 of the firstdecoding stage 51 and, secondly, by the received signal S_(r), fromwhich the extrinsic piece of information a(S_(r)-S_(e)), namely S_(r)(1−α)+αS_(e) has been extracted.

The coefficient α is preferably chosen to be close to 0.25. In onealternative embodiment, the value of the coefficient α is optimized as afunction of the signal-to-noise ratio. In this way, depending on thesignal-to-noise ratio, it may be chosen to place greater or lowerconfidence in the estimation 520 of the symbol sent, to take account ofit in varying degrees during the second decoding iteration, andespecially during the decoding of the most robust MSB level.

Thus, if the signal-to-noise ratio is very good, a will be chosen to beclose to 1. If not, a will be chosen to be close to 0.

Such an optimization of α can be preceded especially by a step fordetermining the signal-to-noise ratio, by means of pilot values,inserted into the signal sent. According to a prior art technique, thepilots constitute reference information whose value is known a priori tothe receiver. By comparing this predetermined value of the pilots withthe value of the received pilots, the receiver may estimate the transferfunction of the transmission channel, and hence the signal-to-noiseratio affecting the sent signal, by division. This technique furthermoremakes it possible to assess the robustness of the different codinglevels.

After demodulation by the block referenced 521, new demodulated bits{tilde over (b)}₃ ^(i), i=1, . . . , n, are obtained. These newdemodulated bits are improved relative to the corresponding bits comingfrom the demodulation block referenced 511, owing to the fact that theextrinsic information and the result of the decoding of the less robustLSB and ISB levels of the first decoding stage 51 are jointly taken intoaccount.

These demodulated bits {tilde over (b)}₃ ^(i), i=1, . . . , n, are fedinto the decoder referenced 524, which delivers the improved decodedbits {circumflex over (b)}₃ ^(i), i=1, . . . , n. As above, these bitsare re-coded by the coder, identical to the one used at transmission,referenced 527, and then fed into the demodulation device of the ISBlevel referenced 522. This demodulation device 522 is furthermore fed atinput by the difference between the received symbol and the extrinsicinformation, in the form S_(r) (1−α)+αS_(e), and by the re-coded bits ofthe less robust LSB level, coming from the coder referenced 519.

The ISB demodulator 522 delivers the demodulated intermediatesignificant bits {tilde over (b)}₂ ^(i), i=1, . . . , n, which feed thedecoder referenced 525 delivering {circumflex over (b)}₂ ^(i) improveddecoded bits {circumflex over (b)}₂ ^(i), i=1, . . . , n.

Again, these bits {circumflex over (b)}₂ ^(i) i=1, . . . , n arere-coded by means of the coder, identical to the one used attransmission, referenced 528, and are then given at the input of theleast robust LSB level referenced 523. This demodulation blockreferenced 523 is furthermore fed with the difference between thereceived symbol and the extrinsic information, in the form S_(r)(1−α)+αS_(e). It therefore delivers demodulated bits {tilde over (b)}₁^(i), i=1, . . . , n, improved with respect to the corresponding bitscoming from the first decoding stage referenced 513, which feed thedecoder referenced 526, this decoder delivering the improved decodedbits {circumflex over (b)}₁ ^(i), i=1, . . . , n.

The implementation of these two successive decoding iterations,conjugated with the use of a piece of extrinsic information, givesimproved performance as compared with prior art techniques, andespecially as compared with the sub-optimal step-by-step decoding methodconditionally implemented for the decoding of signals modulatedaccording to a multi-level coding technique.

This performance is illustrated by the curves of FIG. 6, respectivelypresenting the binary error rate obtained, as a function of thesignal-to-noise S/N ratio, firstly for the decoding method of theinvention and, secondly, for the sub-optimal decoding method of theprior art.

Thus, it is seen that the curve referenced 61 for the binary error rateobtained by the invention decreases far more rapidly, as a function ofthe S/N ratio, than the binary error rate (BER) curve referenced 62obtained by the prior art step-by-step decoding method.

In the context of the DRM consortium presented here above, it wasestablished that the binary error rate BER of 10⁻⁴ constituted theoperating threshold of the system. It will be noted, referring to FIG.6, that a gain of about 2 dB is obtained, for this threshold of 10⁻⁴,between the decoding technique of the prior art and the decoding methodof the invention.

The performance of the system of the invention could be further improvedrelative to the Doppler-affected transmission channel, especially byadding an interleaver, on each encoding level, at transmission. Thereceiver of FIG. 5 would then include a de-interleaving means, whichwould be implemented, for each level, after the demodulation and beforethe decoding.

It will be noted that any type of code can be used in the invention, andespecially turbo-codes. In particular, it is possible to envisage theimplementation of a turbo-code for each of the coding levels.

1. A method of decoding a signal modulated according to a multi-levelcoding technique, comprising at least two coding levels each having adistinct robustness to noise, said signal comprising a plurality ofsymbols (S_(r)) each comprising at least one bit, assigned to one ofsaid coding levels, said method comprising: performing at least twosuccessive decoding iterations with a decoder, each iteration comprisingsuccessive steps of decoding each of said at least one bit, at least oneof the successive steps of decoding taking into account the result of atleast one possible preceding step of decoding; determining therobustness to noise of said coding levels, the robustness to noise of acoding level being inversely proportional to the error rate of saidcoding level; and determining a decoding order according to therobustness to noise of said coding levels, wherein, during said decodingiterations, said bits ({tilde over (b)}₃ ^(i), {tilde over (b)}₂ ^(i),{tilde over (b)}₁ ^(i)) are decoded according to said decoding order,said at least one bit assigned to one of said coding levels having agreatest robustness to noise, referred to as a most robust coding level,being decoded first.
 2. The method of decoding according to claim 1,wherein said decoding order corresponds to the decreasing order of therobustness to noise of the coding levels to which said at least one bitis assigned.
 3. The method of decoding according to claim 1, whereineach of said successive steps of decoding takes into account the resultof said preceding step or steps of decoding so as to improve the resultof said successive steps for the decoding of said bits assigned to theless robust coding levels.
 4. The method of decoding according to claim1, wherein said bits assigned to said most robust coding level are mostsignificant bits of a corresponding symbol.
 5. The method of decodingaccording to claim 1, wherein within one of said iterations of decoding,each of said successive steps of decoding of said at least one bit ispreceded by a corresponding demodulation step.
 6. The method of decodingaccording to claim 1, wherein a step of decoding the bits of a givenlevel takes into account, during the n^(th) decoding iteration, wheren≧2, the result of at least certain of said successive steps of decodingof said at least one bit assigned to the coding levels less robust thansaid given level, and implemented during at least one of said precedingiterations.
 7. The method of decoding according to claim 6, wherein atthe end of at least certain of said decoding iterations, the methodimplements a step of estimating a sent symbol S_(e), and a step ofcalculating an extrinsic information taking into account said estimatedsent symbol.
 8. The method of decoding according to claim 7, whereinsaid extrinsic information has the form α(S_(r)-S_(e)), where α∈[0, 1],S_(r) is a received symbol and S_(e) is said estimated sent symbol. 9.The method of decoding according to claim 8, wherein α is substantiallyequal to 0.25.
 10. The method of decoding according to claim 8, themethod further comprising a step of optimizing the value of α accordingto a signal-to-noise ratio.
 11. The method of decoding according toclaim 10, the method further comprising a step of estimating thesignal-to-noise ratio from at least one sent reference information item,referred to as a pilot, whereof the value is known a priori inreception.
 12. The method of decoding according to claim 6, whereinwithin one of said iterations of decoding, each of said successive stepsof decoding of said at least one bit is preceded by a correspondingdecoding step, the method further comprising, for at least certain ofsaid coding levels, an additional step of de-interleaving implementedbetween said steps of demodulating and decoding of said at least onebit.
 13. The method of decoding according to claim 1, wherein saidperforming step implements two successive decoding iterations.
 14. Themethod of decoding according to claim 1, the method further comprising astep of receiving, by a receiver, prior to performing the decodingiterations, the signal modulated according to the multi-level codingtechnique, comprising at least two coding levels, each having thedistinct robustness to noise.
 15. The method of decoding according toclaim 1, wherein said robustness to noise of the coding levels isdetermined by decoding each decoding level independently.
 16. The methodof decoding according to claim 1, wherein said robustness to noise ofthe coding levels is determined by decoding each decoding levelindependently in order to determine the most robust coding level, thendecoding the other coding levels taking into account the most robustcoding level.
 17. A device for receiving a signal modulated according toa multi-level coding technique, comprising at least two coding levelseach having a distinct robustness to noise, said signal comprising aplurality of symbols each comprising at least one bit, assigned to oneof said coding levels, said device comprising decoding means forimplementing at least two successive decoding iterations each comprisingsuccessive steps of decoding each of said bits ({tilde over (b)}₃ ^(i),{tilde over (b)}₂ ^(i), {tilde over (b)}₁ ^(i)), at least one of saidsuccessive steps of decoding taking into account the result of at leastone possible preceding step of decoding; means for determining therobustness to noise of said coding levels, the robustness to noise of acoding level being inversely proportional to the error rate of saidcoding level; and means for determining a decoding order according tothe robustness to noise of said coding levels, wherein, during saiddecoding iterations, said decoding means decode said bits according tosaid decoding order taking into account the robustness to noise of saidcoding levels, the bit or bits assigned to the coding level having agreatest robustness to noise, referred to as a most robust coding level,being decoded first.
 18. The device according to claim 17, wherein saidmeans for determining the robustness to noise of said coding levelsdecode each decoding level independently.
 19. The device according toclaim 17, wherein said means for determining the robustness to noise ofsaid coding levels decode each decoding level independently in order todetermine the most robust coding level, then decode the other codinglevels taking into account the most robust coding level.
 20. The deviceaccording to claim 17, wherein said decoding order corresponds to thedecreasing order of the robustness to noise of the coding levels towhich said at least one bit is assigned.
 21. The device according toclaim 17, wherein said decoding means for implementing the at least twosuccessive decoding iterations takes into account the result of apreceding step or steps of decoding so as to improve the result of saidsteps for the decoding of said bits assigned to the less robust codinglevels.
 22. The device according to claim 17, wherein said bits assignedto said most robust coding level are most significant bits of acorresponding symbol.
 23. The device according to claim 17, said devicefurther comprising means for demodulating and de-interleaving, activatedbefore each of said successive steps of decoding within one of saiditerations of decoding.
 24. The device according to claim 17, whereinsaid decoding means decode the bits of a given level taking intoaccount, during the n^(th) decoding iteration, where n≧2, the result ofat least certain of said successive steps of decoding of said at leastone bit assigned to the coding levels less robust than said given level,and implemented during at least one of said preceding iterations. 25.The device according to claim 24, wherein at the end of at least certainof said iterations, said decoding means estimates a sent symbol S_(e),and calculates an extrinsic information taking into account saidestimated send symbol.
 26. The device according to claim 25, whereinsaid extrinsic information has the form α(S_(r)-S_(e)), where α∈[0, 1],S_(r) is a received symbol and S_(e) is said estimated sent symbol. 27.The device according to claim 26, wherein α is substantially equal to0.25.
 28. The device according to claim 26, the device furthercomprising means for optimizing the value of α according to asignal-to-noise ratio.
 29. The device according to claim 28, the devicefurther comprising means for estimating the signal-to-noise ratio fromat least one sent reference information item, referred to as a pilot,whereof the value is known a priori in reception.
 30. The deviceaccording to claim 17, wherein said decoding means implements twosuccessive decoding iterations.
 31. A system for coding/decoding of asignal comprising a plurality of symbols each comprising at least onebit, wherein the system comprises: at least one coding device enablingthe modulation of said signal according to a multi-level codingtechnique, comprising at least two coding levels each having a distinctrobustness to noise, each of said bits being assigned to one of saidcoding levels; and at least one decoding device comprising: decodingmeans for implementing at least two successive decoding iterations eachcomprising successive steps of decoding each of said at least one bit,at least one of said successive steps of decoding taking into accountthe result of at least one, possible preceding step of decoding; meansfor determining the robustness to noise of said coding levels, therobustness to noise of a coding level being inversely proportional tothe error rate of said coding level; and means for determining adecoding order according to the robustness to noise of said codinglevels, wherein, during said decodes iterations, said decoding meansdecoding said bits according to said decoding order taking into accountthe robustness to noise of said coding levels, the bit or bits assignedto the coding level having a greatest robustness to noise, referred toas a most robust coding level, being decoded first.
 32. A method ofreceiving a signal modulated according to a multi-level coding techniquecomprising at least two coding levels each having a distinct robustnessto noise, said signal comprising a plurality of symbols (S_(r)) eachcomprising at least one bit, assigned to one of said coding levels, saidmethod comprising: performing at least two successive decodingiterations with a decoder, each iteration comprising successive steps ofdecoding each of said at least one bit, at least one of said successivesteps of decoding taking into account the result of at least onepossible preceding step of decoding; determining the robustness to noiseof said coding levels, the robustness to noise of a coding level beinginversely proportional to the error rate of said coding level; anddetermining a decoding order according to the robustness to noise ofsaid coding levels, wherein the steps of performing at least twodecoding iterations, determining the robustness to noise of said codinglevels, and determining the decoding order are performed within at leastone of the following fields: digital radio transmissions, in particularof the DRM (Digital Radio Mondiale) type; error correction codes;digital signal processing; digital communications; recording/restorationof a digital signal, wherein, during said decoding iterations, said bitsare decoded according to said decoding order taking into account therobustness to noise of said coding levels, the bit or bits assigned tothe coding level having a greatest robustness to noise, referred to as amost robust coding level, being decoded first.